curve #3807

y² = x³ − x² − 2101701481499716920x + 424712008818857940028031232

a-invariants: [0, -1, 0, -2101701481499716920, 424712008818857940028031232]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 2100709764345912720
discriminant (Δ): 516221560799714061757517055378297827251018033415813760000
Faltings height: 9.5749
naive height: 138.1814
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 47, 79, 97, 131, 5009
regulator: 16454.492074831547238302139931805168490389950524176
submitted by: Daniel Błażewicz
submitted at: 2026-10-02 11:16:06 UTC
last updated: 2026-10-02 11:16:06 UTC

(-694802356, 39364490265100)
(-29299562, 22051435079190)
(70336327814, 18649943970327670)
(-404416292066/441, 368217480259567070/9261)
(2163337881093/1444, 1386650938559799627/54872)
(28344750383104/16641, 90736763994330454000/2146689)

(u,v) = (53641,33605) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.

last edited by Daniel Błażewicz at 2026-10-02 11:16:06 UTC · history